Federer, a two-time champion in Doha, routed sixth-seeded Viktor Troicki 6-2, 6-2 in just 65 minutes and will face third-seeded Jo-Wilfried Tsonga in the semifinals. Top-ranked Nadal was given more of a test by Latvia's Ernests Gulbis before he came through 7-6 (3), 6-3.
"It is always a difficult match against him," Nadal said. "You have to play special against him. I did my best today and I am happy about it. ... I pushed him hard and broke him many times. I am playing well. My target here is to win."
Nadal plays defending champion Nikolay Davydenko or Ivo Karlovic on Friday.
The Spaniard broke Gulbis in the fourth game of the first set and, although Gulbis broke back, the 22-year-old Latvian could not maintain his form in the tiebreaker and Nadal won four points in a row to take it.
On Wednesday, Nadal dropped the second set 6-0 against Lukas Lacko after taking the first on a tiebreaker, but there was no repeat against Gulbis. He broke twice more to win easily.
Federer, who won the title in 2005 and 2006, had little trouble improving his win-loss record at the tournament to 21-3. He broke Troicki twice in each set while holding serve easily against a tired-looking opponent who has won just one ATP title.
The No. 2-ranked Federer did not serve a single ace but did not have to save a break point as he kept up his record of not dropping a set in the tournament.
"Look, I am happy with my form here and in this match," Federer said. "It wasn't a tough match and I was quite comfortable. ... I was in control of my shots and created many opportunities. This was easy compared to the first two matches."
Tsonga outlasted seventh-seeded Guillermo Garcia-Lopez of Spain 7-6 (4), 7-6 (9) to continue his successful comeback from a knee injury that brought his 2010 season to an early end.
Federer has won two of his three previous meetings with the Frenchman.
"He's a wonderful player, a great character," Federer said. "He has performed well at the big tournaments, especially on the hard surface at the Australian Open.
"Unfortunately, he's had injuries and didn't play as much but he's tough."